{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression for Binary responses: Alternative link functions\n",
    "\n",
    "In this example we use a simple dataset to fit a Generalized Linear Model for a binary response using different link functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import bambi as bmb\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.special import expit as invlogit\n",
    "from scipy.stats import norm\n",
    "\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generalized linear models for binary response\n",
    "\n",
    "First of all, let's review some concepts. A Generalized Linear Model (GLM) is made of three components.\n",
    "\n",
    "**1. Random component**\n",
    "\n",
    "A set of independent and identically distributed random variables $Y_i$. Their (conditional) probability distribution belongs to the same family $f$ with a mean given by $\\mu_i$. \n",
    "\n",
    "**2. Systematic component (a.k.a linear predictor)**\n",
    "\n",
    "Constructed by a linear combination of the parameters $\\beta_j$ and explanatory variables $x_j$, represented by $\\eta_i$\n",
    "\n",
    "$$\n",
    "\\eta_i = \\mathbf{x}_i^T\\mathbf{\\beta} = x_{i1}\\beta_1 + x_{i2}\\beta_2 + \\cdots + x_{ip}\\beta_p\n",
    "$$\n",
    "\n",
    "**3. Link function**\n",
    "\n",
    "A monotone and differentiable function $g$ such that \n",
    "\n",
    "$$\n",
    "g(\\mu_i) = \\eta_i = \\mathbf{x}_i^T\\mathbf{\\beta}\n",
    "$$\n",
    "where $\\mu_i = E(Y_i)$\n",
    "\n",
    "As we can see, this function specifies the link between the random and the systematic components of the model.\n",
    "\n",
    "An important feature of GLMs is that no matter we are modeling a function of $\\mu$ (and not just $\\mu$, unless $g$ is the identity function) is that we can show predictions in terms of the mean $\\mu$ by using the inverse of $g$ on the linear predictor $\\eta_i$\n",
    "\n",
    "$$\n",
    "g^{-1}(\\eta_i) = g^{-1}(\\mathbf{x}_i^T\\mathbf{\\beta}) = \\mu_i\n",
    "$$\n",
    "\n",
    "\n",
    "In Bambi, we can use `family=\"bernoulli\"` to tell we are modeling a binary variable that follows a Bernoulli distribution and our random component is of the form\n",
    "\n",
    "$$\n",
    "Y_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{with probability } \\pi_i \\\\\n",
    "        0 & \\textrm{with probability } 1 - \\pi_i \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "that has a mean $\\mu_i$ equal to the probability of success $\\pi_i$.\n",
    "\n",
    "By default, this family implies $g$ is the **logit function**.\n",
    "\n",
    "$$\n",
    "\\begin{array}{lcr}    \n",
    "    \\displaystyle \\text{logit}(\\pi_i) = \\log{\\left( \\frac{\\pi_i}{1 - \\pi_i} \\right)} = \\eta_i &\n",
    "    \\text{ with } &\n",
    "    \\displaystyle g^{-1}(\\eta) = \\frac{1}{1 + e^{-\\eta}} = \\pi_i\n",
    "\\end{array}\n",
    "$$\n",
    "    \n",
    "But there are other options available, like the **probit** and the **cloglog** link functions.  \n",
    "\n",
    "The **probit** function is the inverse of the cumulative density function of a standard Gaussian distribution \n",
    "\n",
    "$$\n",
    "\\begin{array}{lcr}    \n",
    "    \\displaystyle \\text{probit}(\\pi_i) = \\Phi^{-1}(\\pi_i) = \\eta_i &\n",
    "    \\text{ with } &\n",
    "    \\displaystyle g^{-1}(\\eta) = \\Phi(\\eta_i) = \\pi_i\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "And with the **cloglog** link function we have \n",
    "\n",
    "$$\n",
    "\\begin{array}{lcr}    \n",
    "    \\displaystyle \\text{cloglog}(\\pi_i) = \\log(-\\log(1 - \\pi)) = \\eta_i &\n",
    "    \\text{ with } &\n",
    "    \\displaystyle g^{-1}(\\eta) = 1 - \\exp(-\\exp(\\eta_i)) = \\pi_i\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "**cloglog** stands for **complementary log-log** and $g^{-1}$ is the cumulative density function of the extreme minimum value distribution.\n",
    "\n",
    "Let's plot them to better understand the implications of what we're saying."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def invcloglog(x):\n",
    "    return 1 - np.exp(-np.exp(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5, 5, num=200)\n",
    "\n",
    "# inverse of the logit function\n",
    "logit = invlogit(x)\n",
    "\n",
    "# cumulative density function of standard gaussian\n",
    "probit = norm.cdf(x)\n",
    "\n",
    "# inverse of the cloglog function\n",
    "cloglog = invcloglog(x)\n",
    "\n",
    "plt.plot(x, logit, color=\"C0\", lw=2, label=\"Logit\")\n",
    "plt.plot(x, probit, color=\"C1\", lw=2, label=\"Probit\")\n",
    "plt.plot(x, cloglog, color=\"C2\", lw=2, label=\"CLogLog\")\n",
    "plt.axvline(0, c=\"k\", alpha=0.5, ls=\"--\")\n",
    "plt.axhline(0.5, c=\"k\", alpha=0.5, ls=\"--\")\n",
    "plt.xlabel(r\"$x$\")\n",
    "plt.ylabel(r\"$\\pi$\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above we can see both the **logit** and the **probit** links are symmetric in terms of their slopes at $-x$ and $x$. We can say the function approaches $\\pi = 0.5$ at the same rate as it moves away from it. However, these two functions differ in their tails. The **probit** link approaches 0 and 1 faster than the **logit** link as we move away from $x=0$. Just see the orange line is below the blue one for $x < 0$ and it is above for $x > 0$. In other words, the logit function has heavier tails than the probit.\n",
    "\n",
    "On the other hand, the **cloglog** does not present this symmetry, and we can clearly see it since the green line does not cross the point (0, 0.5). This function approaches faster the 1 than 0 as we move away from $x=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data\n",
    "\n",
    "We use a data set consisting of the numbers of beetles dead after five hours of exposure to gaseous carbon disulphide at various concentrations. This data can be found in _[An Introduction to Generalized Linear Models](https://doi.org/10.1201/9781315182780) by A. J. Dobson and A. G. Barnett_, but the original source is (Bliss, 1935)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Dose, $x_i$ <br />($\\log_{10}\\text{CS}_2\\text{mgl}^{-1}$)| Number of beetles, $n_i$ | Number killed, $y_i$ |\n",
    "| --- | --- | --- |\n",
    "| 1.6907 | 59 | 6 |\n",
    "| 1.7242 | 60 | 13 |\n",
    "| 1.7552 | 62 | 18 |\n",
    "| 1.7842 | 56 | 28 |\n",
    "| 1.8113 | 63 | 52 |\n",
    "| 1.8369 | 59 | 53 |\n",
    "| 1.8610 | 62 | 61 |\n",
    "| 1.8839 | 60 | 60 |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a data frame where the data is in long format (i.e. each row is an observation with a 0-1 outcome)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1.6907, 1.7242, 1.7552, 1.7842, 1.8113, 1.8369, 1.8610, 1.8839])\n",
    "n = np.array([59, 60, 62, 56, 63, 59, 62, 60])\n",
    "y = np.array([6, 13, 18, 28, 52, 53, 61, 60])\n",
    "\n",
    "data = pd.DataFrame({\"x\": x, \"n\": n, \"y\": y})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build the models\n",
    "\n",
    "Bambi has two families to model binary data: Bernoulli and Binomial. The first one can be used when each row represents a single observation with a column containing the binary outcome, while the second is used when each row represents a group of observations or realizations and there's one column for the number of successes and another column for the number of trials. \n",
    "\n",
    "Since we have aggregated data, we're going to use the Binomial family. This family requires using the function `proportion(y, n)` on the left side of the model formula to indicate we want to model the proportion between two variables. This function can be replaced by any of its aliases `prop(y, n)` or `p(y, n)`. Let's use the shortest one here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = \"p(y, n) ~ x\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Logit link\n",
    "\n",
    "The logit link is the default link when we say `family=\"binomial\"`, so there's no need to add it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [Intercept, x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc6c6bbdc2b645578cb0b7d3f8cf18a4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "model_logit = bmb.Model(formula, data, family=\"binomial\")\n",
    "idata_logit = model_logit.fit(draws=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probit link"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [Intercept, x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d6a024a7be8940ff969f2b3cb7d63a6b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "model_probit = bmb.Model(formula, data, family=\"binomial\", link=\"probit\")\n",
    "idata_probit = model_probit.fit(draws=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: p(y, n) ~ x\n",
       "        Family: binomial\n",
       "          Link: p = probit\n",
       "  Observations: 8\n",
       "        Priors: \n",
       "    target = p\n",
       "        Common-level effects\n",
       "            Intercept ~ Normal(mu: 0.0, sigma: 1.5)\n",
       "            x ~ Normal(mu: 0.0, sigma: 15.848)\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_probit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cloglog link"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [Intercept, x]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d8f22df024604ce38f3c9d78b75bc509",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "model_cloglog = bmb.Model(formula, data, family=\"binomial\", link=\"cloglog\")\n",
    "idata_cloglog = model_cloglog.fit(draws=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "We can use the samples from the posteriors to see the mean estimate for the probability of dying at each concentration level. To do so, we use a little helper function that will help us to write less code. This function leverages the power of the new `Model.predict()` method that is helpful to obtain both in-sample and out-of-sample predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_predictions(model, idata, seq):\n",
    "    # Create a data frame with the new data\n",
    "    new_data = pd.DataFrame({\"x\": seq})\n",
    "    \n",
    "    # Predict probability of dying using out of sample data\n",
    "    model.predict(idata, data=new_data)\n",
    "    \n",
    "    # Get posterior mean across all chains and draws\n",
    "    mu = idata.posterior[\"p\"].mean((\"chain\", \"draw\"))\n",
    "    return mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_seq = np.linspace(1.6, 2, num=200)\n",
    "\n",
    "mu_logit = get_predictions(model_logit, idata_logit, x_seq)\n",
    "mu_probit = get_predictions(model_probit, idata_probit, x_seq)\n",
    "mu_cloglog = get_predictions(model_cloglog, idata_cloglog, x_seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y / n, c = \"white\", edgecolors = \"black\", s=100)\n",
    "plt.plot(x_seq, mu_logit, lw=2, label=\"Logit\")\n",
    "plt.plot(x_seq, mu_probit, lw=2, label=\"Probit\")\n",
    "plt.plot(x_seq, mu_cloglog, lw=2, label=\"CLogLog\")\n",
    "plt.axhline(0.5, c=\"k\", alpha=0.5, ls=\"--\")\n",
    "plt.xlabel(r\"Dose $\\log_{10}CS_2mgl^{-1}$\")\n",
    "plt.ylabel(\"Probability of death\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we can see the models using the **logit** and **probit** link functions present very similar estimations. With these particular data, all the three link functions fit the data well and the results do not differ significantly. However, there can be scenarios where the results are more sensitive to the choice of the link function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References**\n",
    "\n",
    "Bliss, C. I. (1935). The calculation of the dose-mortality curve. Annals of Applied Biology 22, 134–167"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Sep 28 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.7\n",
      "IPython version      : 9.4.0\n",
      "\n",
      "pandas    : 2.3.2\n",
      "arviz     : 0.22.0\n",
      "matplotlib: 3.10.6\n",
      "numpy     : 2.3.3\n",
      "bambi     : 0.14.1.dev56+gd93591cd2.d20250927\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dev",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
